The following constraints are derived from the business analysis of departments in an

imaginery state university in Texas. Show how they can be represented in ER model $($if

it can't be represented, state why staff and faculty can have more than one telephone numbers.

$$ Each research student must be supervised by at least two faculty members.

$$ Staff can also be enrolled as research students in the department that he$/$she

works for.

$$ Each faculty member must belong to a department in the university.

$$ Each department should have at least $5$ faculty members.

$$ Each publication of a department can be written by many authors $($faculty

and research students$)$ and the authors are arranged in alphbatical order.

$$ A staff appointment in a depiartment can be fractional or part$-$time.